On 4/3/2010 7:07 AM, Alasdair Urquhart wrote:
> Of course Goedel did not consider his results to be paradoxical.
> This is because he distinguished sharply between truth and
> formal provability -- this distinction of course is the
> heart of the incompleteness theorems.
Goedel was 16 when Skolem pointed out his eponymous paradox in 1922. To
what extent did Russell appreciate Skolem's paradox?
With nine years to reflect on that paradox I would think any reasonable
philosopher would develop a suspicion of any result that depended on
distinguishing truth and provability, since the paradox seems on the
face of it to be arguing against the distinction.
Conversely the sharp nature of Goedel's result under the assumption of
that distinction would tend to reinforce the existence and acceptability
of the distinction while enhancing the paradoxical character of Skolem's
observation.
One might guess that von Neumann as more a mathematician than a
philosopher was less bothered by Skolem's paradox than Russell, assuming
the latter fully appreciated it.
Vaughan Pratt